A198950 G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k / A(x)^k] * x^n/n ).

1, 1, 2, 5, 10, 22, 58, 150, 392, 1097, 3139, 9069, 26903, 81299, 248305, 768521, 2407340, 7607947, 24248690, 77906841, 251995121, 820096599, 2684160567, 8830103123, 29183369411, 96865043941, 322780531149, 1079491353973, 3622338207474, 12193038599714, 41161594789286

Offset: 0

Author

Paul D. Hanna, Oct 31 2011

Keywords

• nonn

Comments

Compare to g.f. G(x) = (1+x^2)/(1-x-x^3) that satisfies:

G(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^2 * x^k / G(x)^k] * x^n/n ).

Examples

			 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 10*x^4 + 22*x^5 + 58*x^6 +...
where
log(A(x)) = (1 + x/A(x))*x + (1 + 2^3*x/A(x) + x^2/A(x)^2)*x^2/2 +
(1 + 3^3*x/A(x) + 3^3*x^2/A(x)^2 + x^3/A(x)^3)*x^3/3 +
(1 + 4^3*x/A(x) + 6^3*x^2/A(x)^2 + 4^3*x^3/A(x)^3 + x^4/A(x)^4)*x^4/4 +
(1 + 5^3*x/A(x) + 10^3*x^2/A(x)^2 + 10^3*x^3/A(x)^3 + 5^3*x^4/A(x)^4 + x^5/A(x)^5)*x^5/5 +...
more explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 19*x^4/4 + 46*x^5/5 + 162*x^6/6 + 477*x^7/7 + 1371*x^8/8 +...